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# If f(x) = x^3 + kx^2 − 4x, what is the value of k?

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Joined: 02 Sep 2009
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If f(x) = x^3 + kx^2 − 4x, what is the value of k?  [#permalink]

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06 Aug 2017, 01:04
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Difficulty:

85% (hard)

Question Stats:

43% (02:20) correct 57% (02:13) wrong based on 52 sessions

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If f(x) = x^3 + kx^2 − 4x, what is the value of k?

(1) f(k) = −f(−k)
(2) f(f(2)) = 0

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Re: If f(x) = x^3 + kx^2 − 4x, what is the value of k?  [#permalink]

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06 Aug 2017, 01:56
Statement 1 alone is sufficient IMO.
As per statement 1: -f(-k) yields x^3-kx^2+4x.
So x^3+kx^2+4x=x^3-kx^2+4x.
Which ultimately yield 0.

Statement 2 gives different values of K.

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Re: If f(x) = x^3 + kx^2 − 4x, what is the value of k?  [#permalink]

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06 Aug 2017, 03:40
Bunuel wrote:
If f(x) = x^3 + kx^2 − 4x, what is the value of k?

(1) f(k) = −f(−k)
(2) f(f(2)) = 0

(1)
$$f(k) = 2k^3 - 4k = -f(-k) = -4k$$
$$k^3 = 0$$
$$k=0$$

Sufficient

(2)
$$f(2) = 4k$$
$$f(f(2)) = 80k^3 -16k = 0$$
$$k = 0,+1/\sqrt{5}, -1/\sqrt{5}$$
Not sufficient

Hence A
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Re: If f(x) = x^3 + kx^2 − 4x, what is the value of k?   [#permalink] 06 Aug 2017, 03:40
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